基于属性论方法与波恩斯坦基函数拟合技术的股市预测算法研究
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摘要
随着经济的发展和人们投资意识的转变，股票已成为现代人生活中的一个重要组成部分，股票投资已成为社会公众谈论的中心之一，而股市的健康发展和繁荣也成为管理者和投资者关心和研究的重点。股票投资的收益与风险往往是成正比的，即投资收益越高，可能冒的风险越大。因此，股市预测方法的研究具有极其重要的应用价值和理论意义。但是股价系统内部结构的复杂性、外部因素的多变性决定了这项任务的艰巨性。
本文在深入分析股票投资理论和股价预测方法的基础上，提出了利用属性论方法和波恩斯坦基函数拟合技术的股市预测算法。该算法充分考虑了历史因素对未来的影响。对于上市时间较长的股票，先将该股票的时间序列划分成若干宽度相等的数据窗口，通过对其股价时间序列进行相似性搜索，找到与当前股票时间序列数据窗口运行轨迹最为相似的数据窗口，这种相似数据窗口可能存在多个也可能没有。如果是第一种情况，即存在多个相似数据窗口，这时再结合市场能量指标(MAV，PSY，OBV)作为二次判断的依据，最终找到最相似数据窗口，并利用数据窗口的滑动模型求出相应的滑动系数，从而预测该股次日的股价。如果是第二种情况或对于新上市的股票，因无历史因素可供参考，则使用波恩斯坦基函数拟合技术，把股票时间序列拟合出来。波恩斯坦基函数具有凸包性并具有一定的泛化能力，这一点可以作为预测算法的另一理论依据。
运用本算法编写的软件对大量的股票进行了实际预测，预测结果令人满意。证明了本算法简单、有效。为了和神经网络方法作个比较，我们还设计了一个遗传神经网络，并用此遗传神经网络对相同的股票进行了相同的预测。在论文的最后提出了一些对本算法改进的思想。
With the economic growth and the conversion of people's investment consciousness, the stock has become an important part of people's life in modern society. The investment in stock has become one of the focuses of public topic. How to keep the development and the boom of stock market has become the emphasis of concern and research of manager and investor. The proceeds of stock investment always equal to the risks. It also means that the good proceed is based on the poor risk of failure .Therefore the study of stock prediction method has great application value and theoretical significance. On the other hand,the complexity of inside structure and levity of exterior complication in system of stock market prediction is a complex problem.
This paper presents a new method based on Attribute Theory and Bernstein Basic Function fitting after thorough study of stock investment and prediction technology. The historical factors on the future stock market have been well considered. For those stocks which have long history, we first devide its time series window into several sub windows of the same length, then a similarity search method is used to find the most similar time series window to the current stock time series window . In fact, such windows may exist more than one or doesn't exist, the stock power indexes are used as the secondary judgment criterion if there are more than one similar windows.Finally,the arm window is successfully found. At this time , the movement coefficients can be obtained by applying the time series window movement model. Now, we can make prediction on the stock. If there is no such similar window or for those new stocks , the Bernstein Basic Fuction fitting technology are used as to simulate the stock time series. The
Bernstein Basic Function has a property of protruding containing, which is another theoretical basis.
From large quantites of prediction experiments on the stock market, we can say that the algorithm presented in this paper proves to be simple and effective. In order to compare with Neural Network method, an inherited Neural Network is designed to do the same job.
At last, some improved ideas are also put forward.
Wanghong (Computer Science and Application)
Directed by Prof. Feng JiaLi
本文在深入分析股票投资理论和股价预测方法的基础上，提出了利用属性论方法和波恩斯坦基函数拟合技术的股市预测算法。该算法充分考虑了历史因素对未来的影响。对于上市时间较长的股票，先将该股票的时间序列划分成若干宽度相等的数据窗口，通过对其股价时间序列进行相似性搜索，找到与当前股票时间序列数据窗口运行轨迹最为相似的数据窗口，这种相似数据窗口可能存在多个也可能没有。如果是第一种情况，即存在多个相似数据窗口，这时再结合市场能量指标(MAV，PSY，OBV)作为二次判断的依据，最终找到最相似数据窗口，并利用数据窗口的滑动模型求出相应的滑动系数，从而预测该股次日的股价。如果是第二种情况或对于新上市的股票，因无历史因素可供参考，则使用波恩斯坦基函数拟合技术，把股票时间序列拟合出来。波恩斯坦基函数具有凸包性并具有一定的泛化能力，这一点可以作为预测算法的另一理论依据。
运用本算法编写的软件对大量的股票进行了实际预测，预测结果令人满意。证明了本算法简单、有效。为了和神经网络方法作个比较，我们还设计了一个遗传神经网络，并用此遗传神经网络对相同的股票进行了相同的预测。在论文的最后提出了一些对本算法改进的思想。
With the economic growth and the conversion of people's investment consciousness, the stock has become an important part of people's life in modern society. The investment in stock has become one of the focuses of public topic. How to keep the development and the boom of stock market has become the emphasis of concern and research of manager and investor. The proceeds of stock investment always equal to the risks. It also means that the good proceed is based on the poor risk of failure .Therefore the study of stock prediction method has great application value and theoretical significance. On the other hand,the complexity of inside structure and levity of exterior complication in system of stock market prediction is a complex problem.
This paper presents a new method based on Attribute Theory and Bernstein Basic Function fitting after thorough study of stock investment and prediction technology. The historical factors on the future stock market have been well considered. For those stocks which have long history, we first devide its time series window into several sub windows of the same length, then a similarity search method is used to find the most similar time series window to the current stock time series window . In fact, such windows may exist more than one or doesn't exist, the stock power indexes are used as the secondary judgment criterion if there are more than one similar windows.Finally,the arm window is successfully found. At this time , the movement coefficients can be obtained by applying the time series window movement model. Now, we can make prediction on the stock. If there is no such similar window or for those new stocks , the Bernstein Basic Fuction fitting technology are used as to simulate the stock time series. The
Bernstein Basic Function has a property of protruding containing, which is another theoretical basis.
From large quantites of prediction experiments on the stock market, we can say that the algorithm presented in this paper proves to be simple and effective. In order to compare with Neural Network method, an inherited Neural Network is designed to do the same job.
At last, some improved ideas are also put forward.
Wanghong (Computer Science and Application)
Directed by Prof. Feng JiaLi
引文
[1] Hafner C, Frohlich J. Generalized function analysis using hybrid evolutionary algorithms. In: Angeline PJ, ed, Proceedings of the Congress on Evolutionary Computation. Piscataway: IEEE Press, 1999.287-294
[2] 杭行．股票投资．河北人民出版社1999：12-55
[3] lba H, Sasaki T. Using genetic programing to predict financial data. [n:Angeline PJ, ed. Proceedings of the Congress on Evolutionary Computation. Piscataway:IEEE Press, 1999.244-251.
[4] E.W. Saad. D.V. Prokhorov and D.C. Wunsch. Comparative Study of Stock Trend Prediction Using Time Delay, Recurrent and Probabilistic Neural Networks IEEE Trans. On Neural Networks. 1998,9(6):1456-1470
[5] XieZhongjie, Wong Heung and Liu Yali, Artifical Neuron Network and Its Application to Financial Forecasting. Acta Scientiarum Naturalium Universitatis Pekingensis. 2001,37(3):421-425
[6] A.N. Refenes, A. Zapranis and G. Francis. Stock Performance Modeling Using Neural Networks: A Comparative Study with Regression Models. Neural Networks, 1994:7(2):375-388
[7] S Zhou, D Popociv, G Schulz-Ekloff. An Improved Learning law for Back-propagation Networks. In 1993 IEEE Internatinal Conference on Neural Networks, San Francisco: IEEE press, 1993:573-579
[8] 孙炎珺．鲁棒自适应BP算法及其在股票价格预测中的应用．硕士学位优秀论文．北京工业大学．2001
[9] Jung-Hua, Jia_Yann Leu. Stock Market Trend Prediction Using ARIMA-based Neural Networks. IEEE, 1996
[10] 李焕荣，李瑛．基于神经网络的股票指数预测．技术经济管理研究．1998，4
[11] Gu Yuqiao, Chen Tianlun, Huang Wuqun. Forecasting of HANG SHENG INDEX Futures based on neural Networks With chaotic algorith. Act Scientic
Naturalium Universitatis Nankaiensis. 2000,3
[12] Jiali Feng. Degree Functions and Fuzzy Artificial Neurons Induced By Qualitative Mapping[C]. Proceedings of International Conference on Fuzzy Information Processing Theory and Application FIP03's. Tsinghua University Press & Springer, March:511-517
[13] Jiali Feng. Conversion Degree Functions Induced By Qualitative Mapping and Fuzzy Artificial Neurons[C], Proceedings of 2003 International Conference on Machine Learning and Cybernetics, IEEE, Inc. Nov:1135-1140
[14] 冯嘉礼．人工神经元的一种定性映射解释．计算机科学，2001，28(9)增刊：248—253
[15] 冯嘉礼．核事故应急决策支持系统与计算机实现研究：[博士论文]中国原子能科学研究院，2001．
[16] Wang Lihu & Feng Jiali et al, Classifying and Learning Based on Qualitative Mapping[C], International Conference on Intelligent Information Technology, ICIIT-02, September:559-563
[17] 冯嘉礼．定性映射诱导的模糊人工神经元和网络．南京大学学报，2003，39(2)：172-181
[18] 李文佩．基于定性映射和转化程度函数的汉字识别．上海海运学院计算机系硕士学位论文，2004年3月
[19] 李德毅，孟海军，史雪梅．隶属云和隶属云发生器．计算机研究与发展，1995，32 (6) 15-20
[20] 张铃，张钹．M-P神经元模型的几何意义及其应用。软件学报1998，9(5)：334-337
[21] 王守觉，王柏南．人工神经网络的多维空间几何分析及其理论．电子学报，2002，30 (1)：1-4
[22] 李洪兴．模糊逻辑系统与前向式神经网络等价．中国科学，2000，30(2)：150-163
[23] 朱建平，李治国．数据挖掘中一种新的预测模型-基函数拟合预测及其在股市中的应用．系统工程理论与实践，2003，(9)
[24] 李庆杨，王能超，易大义编．数值分析．北京：清华大学出版社，2001：21-115
[25]施法中．计算机辅助几何设计与非均匀有理B样条．北京：北京航空航天出版社，1994：76-135
[26]关履泰．计算机辅助几何图形设计．北京：高等教育出版社和施普林格出版社，1994：20-176
[27]An J, Owen A B. Quasi-reg ression. Statistics Department, Stanford University, 1999
[28]Thuan LV, Luc DT. On Sensitivity in linearmultiobjective programming. Journal of Optimization Theory and Application, 2000, 107(3):615-626
[29]Jain A K, Doraic. 3D object recognition: Representation and matching. Statistics and Computing, 2000. 10:167-182
[30]Farin G. Curves and Surfaces for Computer A idea Geometric Design. Printed in the United States of America, 1990:37-109
[31]Endre Pap, Zita Bosnjak, Sasa Bosnjak. Application of fuzzy sets with different t-norms in the interpretation of portfolio matrices in strategic management. Fuzzy Sets and Systems, 2000,11 4:123-131
[32]Jiawei Han，Micheline Kamber著．数据挖掘概念与技术．北京：机械工业出版社，2002：279-285
[33]Richard J. Povinelli. Identifying Temporal Patterns for Characterization and Prediction of Financial Time Series Events. Proceedings of Artificial Networks in Engineering, St. Louis, Missouri, 1999.
[34]C Faloutsos et al. Fast Subsequence Matching in Time Series Database[C]. SIGMOD Conference. 1994:419-429
[35]王洪，冯嘉礼．基于属性论方法的股市预测算法．复旦大学学报正刊(已录用)
[36]边肇祺，张学工等编著．模式识别(第二版) 北京：清华大学出版社，2002：176—228
[37]Refenes A N, Zapranis A, Francis G. Stock performance modeling using neural networks: a comparative study with regression models. Neural Networks, 1994, 7(2):375-388
[38]焦李成．神经网络的应用与研究．西安：西安电子科技大学出版社，1993
[39] Kasparian V, Batur C, Zhang H et al. Davidon least squares-based learning algorithm for training feedforward neural network. Neural Network, 1994,7(4):661-670
[40] 赵建，邬永革等．基于神经网络的股市预测．计算机研究与发展，1996，33(9)：691-695
[41] 赵程．基于遗传神经网络的股市预测，硕士学位优秀论文．北京工业大学，2002
[42] 叶中行，杨利平．上证指数的混沌特性分析．上海交通大学学报，1998，(32)3：129-132
[43] 叶中行，柯春雷，李宁．影响上海股市的因素筛选和统计分析．上海交通大学学报，1998，(32)3：133-135
[44] 叶中行，曹奕剑．Hurst指数在股票市场有效性分析中的应用．系统工程，2001，(19)3：21-24
[2] 杭行．股票投资．河北人民出版社1999：12-55
[3] lba H, Sasaki T. Using genetic programing to predict financial data. [n:Angeline PJ, ed. Proceedings of the Congress on Evolutionary Computation. Piscataway:IEEE Press, 1999.244-251.
[4] E.W. Saad. D.V. Prokhorov and D.C. Wunsch. Comparative Study of Stock Trend Prediction Using Time Delay, Recurrent and Probabilistic Neural Networks IEEE Trans. On Neural Networks. 1998,9(6):1456-1470
[5] XieZhongjie, Wong Heung and Liu Yali, Artifical Neuron Network and Its Application to Financial Forecasting. Acta Scientiarum Naturalium Universitatis Pekingensis. 2001,37(3):421-425
[6] A.N. Refenes, A. Zapranis and G. Francis. Stock Performance Modeling Using Neural Networks: A Comparative Study with Regression Models. Neural Networks, 1994:7(2):375-388
[7] S Zhou, D Popociv, G Schulz-Ekloff. An Improved Learning law for Back-propagation Networks. In 1993 IEEE Internatinal Conference on Neural Networks, San Francisco: IEEE press, 1993:573-579
[8] 孙炎珺．鲁棒自适应BP算法及其在股票价格预测中的应用．硕士学位优秀论文．北京工业大学．2001
[9] Jung-Hua, Jia_Yann Leu. Stock Market Trend Prediction Using ARIMA-based Neural Networks. IEEE, 1996
[10] 李焕荣，李瑛．基于神经网络的股票指数预测．技术经济管理研究．1998，4
[11] Gu Yuqiao, Chen Tianlun, Huang Wuqun. Forecasting of HANG SHENG INDEX Futures based on neural Networks With chaotic algorith. Act Scientic
Naturalium Universitatis Nankaiensis. 2000,3
[12] Jiali Feng. Degree Functions and Fuzzy Artificial Neurons Induced By Qualitative Mapping[C]. Proceedings of International Conference on Fuzzy Information Processing Theory and Application FIP03's. Tsinghua University Press & Springer, March:511-517
[13] Jiali Feng. Conversion Degree Functions Induced By Qualitative Mapping and Fuzzy Artificial Neurons[C], Proceedings of 2003 International Conference on Machine Learning and Cybernetics, IEEE, Inc. Nov:1135-1140
[14] 冯嘉礼．人工神经元的一种定性映射解释．计算机科学，2001，28(9)增刊：248—253
[15] 冯嘉礼．核事故应急决策支持系统与计算机实现研究：[博士论文]中国原子能科学研究院，2001．
[16] Wang Lihu & Feng Jiali et al, Classifying and Learning Based on Qualitative Mapping[C], International Conference on Intelligent Information Technology, ICIIT-02, September:559-563
[17] 冯嘉礼．定性映射诱导的模糊人工神经元和网络．南京大学学报，2003，39(2)：172-181
[18] 李文佩．基于定性映射和转化程度函数的汉字识别．上海海运学院计算机系硕士学位论文，2004年3月
[19] 李德毅，孟海军，史雪梅．隶属云和隶属云发生器．计算机研究与发展，1995，32 (6) 15-20
[20] 张铃，张钹．M-P神经元模型的几何意义及其应用。软件学报1998，9(5)：334-337
[21] 王守觉，王柏南．人工神经网络的多维空间几何分析及其理论．电子学报，2002，30 (1)：1-4
[22] 李洪兴．模糊逻辑系统与前向式神经网络等价．中国科学，2000，30(2)：150-163
[23] 朱建平，李治国．数据挖掘中一种新的预测模型-基函数拟合预测及其在股市中的应用．系统工程理论与实践，2003，(9)
[24] 李庆杨，王能超，易大义编．数值分析．北京：清华大学出版社，2001：21-115
[25]施法中．计算机辅助几何设计与非均匀有理B样条．北京：北京航空航天出版社，1994：76-135
[26]关履泰．计算机辅助几何图形设计．北京：高等教育出版社和施普林格出版社，1994：20-176
[27]An J, Owen A B. Quasi-reg ression. Statistics Department, Stanford University, 1999
[28]Thuan LV, Luc DT. On Sensitivity in linearmultiobjective programming. Journal of Optimization Theory and Application, 2000, 107(3):615-626
[29]Jain A K, Doraic. 3D object recognition: Representation and matching. Statistics and Computing, 2000. 10:167-182
[30]Farin G. Curves and Surfaces for Computer A idea Geometric Design. Printed in the United States of America, 1990:37-109
[31]Endre Pap, Zita Bosnjak, Sasa Bosnjak. Application of fuzzy sets with different t-norms in the interpretation of portfolio matrices in strategic management. Fuzzy Sets and Systems, 2000,11 4:123-131
[32]Jiawei Han，Micheline Kamber著．数据挖掘概念与技术．北京：机械工业出版社，2002：279-285
[33]Richard J. Povinelli. Identifying Temporal Patterns for Characterization and Prediction of Financial Time Series Events. Proceedings of Artificial Networks in Engineering, St. Louis, Missouri, 1999.
[34]C Faloutsos et al. Fast Subsequence Matching in Time Series Database[C]. SIGMOD Conference. 1994:419-429
[35]王洪，冯嘉礼．基于属性论方法的股市预测算法．复旦大学学报正刊(已录用)
[36]边肇祺，张学工等编著．模式识别(第二版) 北京：清华大学出版社，2002：176—228
[37]Refenes A N, Zapranis A, Francis G. Stock performance modeling using neural networks: a comparative study with regression models. Neural Networks, 1994, 7(2):375-388
[38]焦李成．神经网络的应用与研究．西安：西安电子科技大学出版社，1993
[39] Kasparian V, Batur C, Zhang H et al. Davidon least squares-based learning algorithm for training feedforward neural network. Neural Network, 1994,7(4):661-670
[40] 赵建，邬永革等．基于神经网络的股市预测．计算机研究与发展，1996，33(9)：691-695
[41] 赵程．基于遗传神经网络的股市预测，硕士学位优秀论文．北京工业大学，2002
[42] 叶中行，杨利平．上证指数的混沌特性分析．上海交通大学学报，1998，(32)3：129-132
[43] 叶中行，柯春雷，李宁．影响上海股市的因素筛选和统计分析．上海交通大学学报，1998，(32)3：133-135
[44] 叶中行，曹奕剑．Hurst指数在股票市场有效性分析中的应用．系统工程，2001，(19)3：21-24